The former Oasis frontman tweeted he was "absolutely thrilled" to work with "the last rock 'n' roll footballer".
He wrote: "Songs like this don't come around very often and neither do football players like him."
The track features on the former Oasis frontman's second number one solo album Why Me? Why Not.
Director Charlie Lightening's accompanying video begins with "King" Eric summoning "R Kid" to refill his wine glass, before he strolls semi-naked through his palace, glugging wine and tinkling on a grand piano.
He then claims his crown and robe and heads outside, where his humble servant is waiting to open the door of the Rolls Royce.
Image copyrightLightening Films
The grounds of the giant white manor house resemble that of Gallagher's late hero John Lennon, whose Ascot estate featured in the video for Imagine.
Six weeks ago, Cantona - who won four Premier League titles with United - posted a video of himself singing the song while sat on a couch.
"When two Manchester legends meet," wrote Cantona, calling Once his "song of the year".
The 47-year-old singer admitted to Copa90 Football last year that City's bitter rivals, led by Cantona, "ruined my life in the 90s" due to their prolonged success. Although the pendulum has swung the other way in recent years.
After retiring from football in 1997, Cantona went into acting and starred in and co-produced Ken Loach's film Looking For Eric, which premiered at the 2009 Cannes Film Festival.
However, his first role came during his lengthy ban for kicking a Crystal Palace supporter in 1995, when he played a rugby player in the French film Le Bonheur est dans le Pré.
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